{"paper":{"title":"Explicit Brauer-Manin obstructions on plane quartics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brendan Creutz, Nils Bruin","submitted_at":"2026-01-23T18:53:19Z","abstract_excerpt":"We describe a method to show a plane quartic over a number field has no rational points. The method can be adapted to show that a curve does not have divisors of degree 1 or 2 and can be generalized to arbitrary smooth projective curves. Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full $S$-unit group of the \\'etale algebras involved. We illustrate the practicality with several examples, including examples where we determine plane quartics to be of index 2 or 4 when the maximum local index is strictly sma"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full S-unit group of the étale algebras involved.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Brauer-Manin obstruction is assumed to be the dominant or only obstruction that needs to be made explicit, and the adaptation to divisors of degree 1 or 2 is presumed to work without introducing new computational bottlenecks or unaccounted local obstructions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A computational method uses explicit Brauer-Manin obstructions to obstruct rational points on plane quartics without requiring full S-unit group calculations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4a4adae5c736ef3581b29fbb6a78e8f53e300bc2086f5d40aed1a927fcc9398f"},"source":{"id":"2601.16975","kind":"arxiv","version":2},"verdict":{"id":"5d3a0aad-ae2e-4ad9-9f4c-36f073c35213","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:30:08.329096Z","strongest_claim":"Our approach significantly improves on the applicability over previous 2-cover descent methods by not requiring the computation of the full S-unit group of the étale algebras involved.","one_line_summary":"A computational method uses explicit Brauer-Manin obstructions to obstruct rational points on plane quartics without requiring full S-unit group calculations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Brauer-Manin obstruction is assumed to be the dominant or only obstruction that needs to be made explicit, and the adaptation to divisors of degree 1 or 2 is presumed to work without introducing new computational bottlenecks or unaccounted local obstructions.","pith_extraction_headline":"A method makes Brauer-Manin obstructions explicit on plane quartics without computing full S-unit groups of étale algebras."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9275738a975ea2c210837bb212e6dc735561fc1fc122411423d454505195627c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}